Reconstructing the surface of a three-dimensional object can provide information useful for a variety of applications such as generating computer aided design models from physical objects, or outlining biological structures or organs. From the reconstructions, a variety of measurements can be made of the object's dimensions and shape, for example, for use in product development or in scientific investigation. Alternatively, the reconstructions can be used to guide the manufacturing of facsimiles of the object.
A number of reconstruction algorithms have been developed. They fit into two main types. Implicit reconstruction methods attempt to find a smooth function whose value approaches zero when the reconstructed surface fits the input data points most closely. These methods differ in the form of the function, and in the measure of closeness of fit. The disadvantage of this approach is the risk that spurious surface components not supported by the data may be generated. A second type of reconstruction algorithm uses parametric techniques. Parametric reconstruction techniques represent a reconstructed surface as a topological embedding function of a two-dimensional parameter domain into a three-dimensional surface. Previous work has concentrated on domain spaces with simple topology, e.g., the plane and the sphere. This simplification of the problem may have the disadvantage of constraining shapes into variants of a geometric figure, making it difficult to fit a modeled surface to more complex shapes.
Regardless of type, reconstruction algorithms are generally developed to address specific problems. They make use of, and hence assume, a partial structure in the data. For example, algorithms that reconstruct a surface from contours generated by slicing the object and stacking the outlines of the object from the slices depend on the fact that the data are organized into closed polygons lying in parallel planes. Attempting to reconstruct a surface without prior assumptions regarding the spatial relationships of the data points derived from that surface has a practical advantage in that the algorithm employed is general purpose and widely applicable. One method that does not make any assumption concerning the structure of the data points is described in a paper entitled "Surface Reconstruction from Unorganized Points" by Hughes Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle (Computer Graphics, 26, Jul. 2, 1992). A subsequent report by these authors describes a modification of their reconstruction algorithm to achieve "Mesh Optimization" (Computer Graphics Proceedings, Annual Conference Series, 1993) in which the reconstruction surface is represented by a small number of vertices without losing shape fidelity. A third report, "Piecewise Smooth Surface Reconstruction" by Hughes Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Hubert Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle (Computer Graphics Proceedings, Annual Conference Series, 1994) describes further modification of the reconstruction method for unorganized points in which the surface can be represented in terms of piecewise smooth surface models. This improvement allows the modeling of surfaces of arbitrary topological type, with recovery of sharp features such as creases and comers.
The approach of Hoppe et al. has been successful for input point data sets, which include points that are densely and evenly sampled and are thus extremely accurate, e.g., data sets produced by laser scanners. However, such high quality data are not always available. For example, in medical imaging, the number of data points may be limited by procedural risk to the patient from radiation exposure, the time required to obtain the images, the resolution of the imaging equipment, or by restrictions on computer memory or required processing speed. For such applications, the ability to generate surface reconstructions with high spatial shape fidelity from sparse data would be useful, but a method to achieve this result is not disclosed in the prior art.
Another limitation of currently available reconstruction algorithms is the generality of the description. Both implicit and parametric approaches generate a global description of the three-dimensional surface, the representation that best fits all of the input point data. However, in some applications, it would be useful to identify the part of the reconstruction that corresponds to a particular subset of input data points. For example, in processing data from images of a human face, it may be useful to designate a subset of input data points as corresponding to an anatomic feature such as a mouth, and to be able to locate the part of the completed reconstruction that was fit to that feature's data points. In addition, the ability to constrain the points corresponding to a feature to a certain part of the reconstruction would be useful. This capability would facilitate, for example, the comparison of a plurality of objects of the same class, by registering them spatially according to the selected features.
One application in medicine that would require these types of functionality in a reconstruction algorithm is reconstructing the surface of the heart. The heart is a complex three-dimensional organ normally having four chambers and four valves. Disease processes can affect any number of these chambers and valves, altering their structure and/or function. Measuring the size, shape, and function of the chambers and valves provides useful information that can assist a physician in evaluating the effect of disease processes, hemodynamic changes, and other influences on the heart. Such measurements may help in diagnosing cardiac problems in patients, evaluating the effect of treatment, assessing prognosis, and in understanding the underlying mechanisms of the disease process and its response to therapeutic interventions.
Most commonly, the left ventricle of the heart is investigated. The left ventricle is of greatest importance to health, because it pumps blood through the body. The right ventricle is also studied, because it provides the impetus for blood circulation through the lungs. One of the most commonly used parameters for diagnostic purposes is the ventricular chamber volume. Patients with diseased hearts may have an enlarged left ventricle, particularly at advanced stages of the disease. The most commonly used parameter of heart function is the ejection fraction, which expresses the proportion of chamber volume ejected with each heart beat, and by reconstructing the surface of the heart, this parameter can more readily be determined.
The reconstructed surface of the heart can also be used for the purpose of monitoring certain parameters indicative of the function of the left ventricle of the heart. These parameters may be used in evaluating a patient's condition during surgical procedures. Other important parameters include the range of motion of the left ventricular wall and the thickening of the ventricular wall, both of which are indicators of coronary heart disease, and of other disease entities. In addition, the shape of the ventricle provides information regarding its status, as the left ventricle becomes more spherical under certain loading conditions. These parameters also provide information that can be used to detect coronary heart disease and other medical problems of the heart. All of these parameters--volume, shape, ejection fraction, wall motion, and wall thickening, rely on having an accurate representation of the ventricular surface.
The effects of coronary heart disease are regional, being limited to the portion of the heart muscle receiving blood supply from an affected artery. When the internal diameter of an artery is reduced by atherosclerotic plaque, blood flow to the specific region of the heart supplied by that artery is restricted. As a result, some degree of dysfunction occurs in the affected heart muscle. During a heart attack, the affected muscle dies and is replaced by scar tissue, which is non-contractile. Thus, the progress of coronary artery disease is revealed by its effect on regional left ventricular function, and the severity of a heart attack is measured by the size of the dysfunctional region and by the extent of the dysfunction. Similarly, any improvement of regional function in the affected portion of the left ventricle is an indication of the effectiveness of a prescribed treatment.
The appearance of dysfunction in a previously well-functioning ventricle is a serious warning that the blood supply is insufficient. Should a deterioration of function occur during surgery, it may be construed as an indication that the anesthesiologist should increase the fluid volume and/or engage in other corrective measures. The detection of regional dysfunction has also been used during stress studies, wherein a patient's heart is imaged using ultrasound while at rest and after exercise, to determine whether the patient's arteries, which may have been open sufficiently while at rest, provide inadequate blood flow during exercise. The degree of dysfunction after a heart attack has occurred may also be determined to develop a prognosis. For example, patients with serious residual dysfunction after a heart attack are at a higher risk of dying in the first year, and more aggressive treatment may be indicated.
The mitral valve controls the flow of blood entering the left ventricle. Under certain disease processes, the leaflets of the mitral valve may become distorted in size, becoming larger and more redundant. The shape of the leaflets may also vary, particularly when the leaflet size is increased, or when the structures that help to tether the leaflets in their proper position become misaligned, ruptured, or stretched. Variations in leaflet size or shape may affect the ability of the valve to open or close properly.
Previous techniques for evaluating the valves and ventricles have typically relied upon two-dimensional imaging. However, it may be difficult to envision a complex cardiac structure even from multiple two-dimensional images. For example, the approach typically used for imaging the left ventricular wall can introduce significant error due to the failure of the technique to compensate for the angle of the beam relative to the cardiac wall. Furthermore, some modalities of two-dimensional imaging, such as x-ray angiography, provide only one or two projection views of the heart. Even imaging modalities that provide multiple views, i.e., ultrasound, magnetic resonance, and computed tomography, are limited in their ability to clearly localize regional dysfunction of the left ventricle, whose anatomy is difficult to grasp from two-dimensional images without extensive training and experience. Multi-planar two-dimensional imaging also has failed to properly visualize the mitral valve annulus, whose saddle shape was not appreciated until three-dimensional imaging was performed in live patients.
Therefore, it would be useful to have the ability to model the heart in three dimensions. This ability would provide an overall view of an affected region that allows a physician to immediately interpret the extent and degree of dysfunction. Accordingly, several methods have been developed that utilize multiple two-dimensional view data to model the heart in three dimensions. These methods generally utilize a geometric reference figure to which the organ is compared, and are based on a spherical or helical coordinate system. Such coordinate system based methods may be unsuitable in patients whose hearts are distorted by disease, and may be applicable only to the left ventricle, which tends to be more regular and consistent in size and shape than the right ventricle in different patients. Furthermore, these methods are not designed to reconstruct planar structures such as the mitral valve leaflets. Another limitation of currently available reconstruction methods is the inability to referentially model specific portions of the heart for comparison to the corresponding portion of normal, undiseased hearts. Yet the quantitative analysis of regional ventricular function, either by measuring wall motion or wall thickening, requires some means for comparing the results obtained within a given region of a patient's heart with the range observed for the same region in a population of patients having normal hearts.
Regardless of the object of interest, a method that references specific regions of the surface reconstruction to the corresponding input point data so as to provide a specific identification of those regions, and which is generally independent of the size and shape of the object, should improve the applicability of the reconstruction for various applications. In imaging the heart, the ability to identify certain anatomic features on the reconstruction of its surface is useful in analyzing parameters of cardiac function such as wall motion and wall thickening in the region that may be abnormal due to a disease process. Furthermore, a method that references specific regions of the heart to a standard or average cardiac template so as to identify an affected region of a patient's heart (even if abnormal due to disease) should aid in better assessing problems that are diagnosed.
Although much of the preceding discussion has dealt with the medical uses of a reconstructed surface for an organ such as the heart or the left ventricle of the heart, it should be noted that the techniques to achieve a reconstructed surface of an organ have much broader application. It should readily be apparent that a technique enabling limited input data derived from imaging virtually any type of object to be applied in reconstructing the surface of the object, relative to selected features of the object, can be used for numerous other purposes that are completely unrelated to medicine.